In a coordinating anion polymerization using a catalyst system as typified by a Ziegler-Natta catalyst, it is well known that olefin or diene can be homopolymerized. In such a catalyst system, however, it is difficult to copolymerize olefin and diene efficiently. For example, JP-A-2006-503341 (Patent Document 1) describes the copolymerization of olefin and diene, hut there are problems in a method as described in Patent Document 1 that the resulting polymer has the restrictive structure, and a catalytic activity is low, and the molecular weight of the polymer is low, and so on.